Question

Abigail buys a new salt shaker in the shape of a cylinder topped by a hemisphere. The cylinder has a diameter of 6 cm and a height of 10 cm. She pours the salt into the salt shaker, so that it takes up half the total volume of the shaker. Find the depth of the salt.

• A. 3
• B. 9
• C. 6
• D. 12

Answer 1

The correct option is C

6

Let the depth of the salt in the shaker be '$x$'

Volume of salt cellar $=\pi r^{2}h+\frac{2}{3}\pi r^3=\pi \times 3^2\left(10\right)+\frac{2}{3}\pi \times 3^3=108\pi c{m}^3$

Salt occupies half the total volume of the shaker, hence volume of salt occupied by salt is

$\pi r^{2}h=\frac{108\pi }{2}\Rightarrow \pi \left(3^2\right)\left(x\right)=54\pi \Rightarrow x=6cm$

So the salt will be 6 cm deep.